Question
Is there team or player control during a throw in or free throw? I cannot find it in the rule book or the case book!

There is not team or player control during a throw-in. There is player and team control during a free throw.

But only until the ball is released.

control
 

Here are the rule cites:
4-12-1 A player is in control of the ball when he/she is holding or dribbling a live ball inbounds. .....
4-12-2 A team is in control of the ball when a player of the team is in control, ....

Since a player at the free throw line holding or dribbling the ball meets the above requirements, there is BOTH player and team control during this part of the free throw. However, as was noted in another post, once the try is released neither type of control exists for the remainder of the free throw even though the free throw hasn't yet ended. See 4-12-6 below and take note of 4-20-3 The free throw ends when the try is successful, when it is certain the try will not be successful, when the try touches the floor or any player, or when the ball becomes dead.

4-12-6 Neither team control nor player control exists during a dead ball, THROW-IN, a jump ball or when the ball is in flight during a try or tap for goal.

This should clarify the control question about the throw-in.

During a free throw, the ball is live so we have team and player control. But once the ball is shot, there is no control since shooting for basketket consitutes giving up team and player control.